Band brakes which provide reaction elements in automatic transmissions are either of the single wrap or multiple wrap type. The multiple wrap type band is usually a "double wrap" band, although three or more wraps can be used. The band is self-energizing when the direction of torque is from the anchor end toward the apply end. Under these conditions, the force at the anchor end is greater than the force at the apply end of the band by the ratio of e.sup..mu..theta.. Thus, the band anchor force is always greater than the apply load, indicating the self-energizing feature.
If the band torque direction is reversed (de-energized), the apply load at the hydraulic piston end will be greater than the band anchor force and the band will not be able to carry as much torque as it did in the energized direction. The self-energizing feature of a single wrap band is a benefit or asset to transmission design since this feature permits the hydraulic energizing force to be maintained at an acceptable value. Bands also have some of the features of a one-way type brake element, that is, on torque reversal the reaction at the braking element is significantly reduced. The single wrap band having a self-energizing and a self-deenergizing direction will greatly reduce the reaction torque on the gear element when the reaction force is reversed from the energizing direction to the deenergizing direction. Thus, the sensitivity to variations in exact time that the band is released is greatly reduced due to the self-deenergizing feature.
If a gear element in an automatic transmission is to be used for two gear ratios (for example, low forward and reverse), having a forward reaction in one ratio and a reverse reaction in the other ratio, a double wrap band is generally used. These devices are not as sensitive to the deenergizing forces as a single wrap band, because they present a larger force ratio between the apply and the anchor end of the band.
A single wrap band can be used to provide reaction force or torque in a planetary set when the reaction torque levels are significantly different between the two gear ratios to be controlled by the reaction member. For example, the reaction torques for an underdrive ratio (i.e. second forward ratio), is significantly greater than the reaction torque for an overdrive ratio (i.e. fourth ratio). The hydraulic system can easily accommodate the force necessary at the band apply end for the overdrive ratio, even though the reaction is in the deenergizing direction. However, upshifting from one overdrive (fourth) to another overdrive (fifth), can require control sophistication that add to the cost and complexity of manufacture. This upshift condition will magnify any errors in the release timing, since the reaction forces are decreasing in the deenergizing direction but will tend to energize the band in the opposite direction as the shift nears completion.